Optimization algorithms for the Steiner team orienteering problem

• Autor(a) principal: Lucas Assunção de Almeida
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/32558
• topic: Engenharia de produção; Otimização combinatória; Engenharia de produção; Otimização combinatória

The Team Orienteering Problem (TOP) is an NP-hard routing problem in which a fleet of identical vehicles aims at collecting rewards (prizes) available at given locations, while satisfying restrictions on the travel times. In the TOP, each location can be visited by at most one vehicle, and the goal is to maximize the total sum of rewards collected by the vehicles within a given time limit. In our research, we propose a generalization of the TOP, namely the Steiner Team Orienteering Problem (STOP). In the STOP, we provide, additionally, a subset of mandatory locations. In this sense, the STOP also aims at maximizing the total sum of rewards collected within the time limit, but, now, every mandatory location must be visited. As a first contribution, we propose a new commodity-based formulation for the STOP and use it within a cutting-plane scheme. The algorithm benefits from the compactness and strength of the proposed formulation and works by separating five families of valid inequalities, which consist of some general connectivity constraints, classical lifted cover inequalities based on dual bounds, a class of the so-called arc-vertex inference cuts and classes of conflict cuts and clique conflict cuts. To our knowledge, the last three classes of inequalities are also introduced in this work, along with the due proofs of validity. A state-of-the-art branch-and-cut algorithm from the literature of the TOP is adapted to the STOP and used as baseline to evaluate the performance of the cutting-plane. Extensive computational experiments show the competitiveness of the new algorithm while solving several STOP and TOP instances. In particular, it is able to solve, in total, 14 more TOP instances than any other previous exact algorithm and finds nine new optimality certificates. With respect to the new STOP instances introduced in this work, our algorithm solves 31 more instances than the baseline. In this work, we also prove that solely finding a feasible solution for the STOP is NP-hard and propose a Large Neighborhood Search (LNS) heuristic for the problem. The algorithm is provided with initial solutions obtained by means of the matheuristic framework known as Feasibility Pump, which, in our implementation, uses as backbone the commodity-based formulation we propose. The LNS heuristic itself combines classical local searches from the literature of routing problems with a long-term memory component based on Path Relinking. Computational experiments show the efficiency and effectiveness of the proposed heuristic in solving a benchmark of 387 STOP instances. Overall, the heuristic solutions imply an average percentage gap of only 0.54% when compared to the best known bounds. In particular, the heuristic reaches the best previously known bounds on 382 of the 387 instances. Additionally, in 21 of these cases, our heuristic is even able to improve over the best known bounds. At last, the hybrid algorithm obtained from warm starting our cutting-plane algorithm with the LNS heuristic is able to solve to optimality four more TOP instances and seven more STOP instances than the cutting-plane algorithm alone. Additionally, it provides the optimality certificates of five previously unsolved (even by our plain cutting-plane algorithm) TOP instances.